<p>This work proposes a new hyperelastic model specifically designed to improve the mechanical description of human and animal skin subjected to large deformations. The originality of the model lies in the joint integration of the first (I₁) and second (I₂) invariants of the Cauchy-Green strain tensor into the energy function, which allows us to overcome the limitations of classical models (such as those of Fung, Veronda-Westmann or Yeoh), which rely solely on I₁. This improvement allows for a better representation of moderate and equibiaxial deformations, which are important characteristics of the actual behavior of skin. The proposed model was applied to experimental data from uniaxial tensile tests on human, pig, and cat skin, as well as to uniaxial and biaxial data on Treloar rubber. The fits obtained show excellent accuracy, with a coefficient of determination (R²) greater than 0.98 across all data sets. Although it has only three parameters, the model performs comparably to more complex formulations, such as the Beda (2007) and Ogden models, while offering greater robustness in moderate strain regimes. Compared to existing approaches, this new formulation allows for more accurate modelling of the complex hyperelastic behavior of biological soft tissues, while remaining simple and interpretable. It therefore has great potential for application in surgical simulation, skin graft design, and finite element models of skin behavior. By incorporating the second invariant, this model represents a significant advance over Fung’s original formulation.</p>